a \strong mayor\ in the mayor-council system has the authority to\nappoint members of the council.\nmake…

Brief Explanations:

In the mayor - council system, a "strong mayor" has executive authority. Council members are usually elected, not appointed by the mayor, so the first option is incorrect. Law - making is typically the role of the council (legislative), not the mayor (executive), so the second option is wrong. Creating a government charter is a more foundational and often a collective or legislative - like task, not a strong mayor's main role. A strong mayor, with executive power, is responsible for managing city departments (executive functions like administration of city services).

Answer:

D. manage city departments.